New Procedures for Hydrologic Regression and Network Analysis Using Generalized Least Squares In Reply Refer To: April 22, 1987 WGS-Mail Stop 415 OFFICE OF SURFACE WATER TECHNICAL MEMORANDUM NO. 87.08 Subject: PROGRAMS AND PLANS--New Procedures for Hydrologic Regression and Network Analysis Using Generalized Least Squares New procedures for hydrologic regression and network analysis using generalized least squares regression are described in the attached report. These procedures will be of interest to personnel involved in regionalizing streamflow characteristics and evaluating the stream-gaging network. These new procedures are an extension and improvement of procedures known as Network Analysis for Regional Information (NARI) that are documented in U.S. Geological Survey Water-Supply Paper 2178. The generalized least squares program provides many advantages over ordinary least squares regression. The regression coefficients are estimated by taking into consideration the time- sampling error in the dependent variable and the cross correlation between sites. A weighting matrix is computed so that each watershed in the data set is weighted proportional to the accuracy (variance) and cross correlation of the dependent variable. The prediction error for ungaged sites is partitioned into model error and sampling error (including both time- and spatial-sampling errors). The model error is that portion of the total error (prediction error) that cannot be reduced by additional data collection. On the other hand, the sampling error can be reduced by operating the existing stations longer, or by installing new stations, or some combination of both. This approach to error analysis makes generalized least squares regression a useful tool for network design and analysis. Using generalized least squares, it is possible to determine the existing or proposed stations that are most important in reducing the sampling error. This provides the data manager with a tool to determine the specific stations (including proposed stations) that are providing the most information in a regional sense. Additional input data are needed in the generalized least squares over that required in ordinary least squares regression. The preparation of this input data is time consuming if done manually. Therefore, ANNIE, an interactive data processor, is being used to prepare these input files. ANNIE and the associated Watershed Data Management (WDM) File is used for Office of Surface Water application programs and provides a mechanism for not only preparing the input data but also to store and manipulate data, make transformations, prepare tables and plots, and guide the user through the analysis. ANNIE/WDM has been developed for several years, and new features are continually added to the system. The development of this system is being coordinated by Alan Lumb, Office of Surface Water, and its purpose is to facilitate hydrologic analyses and particularly the use of hydrologic and hydraulic models. The ANNIE/WDM system is also very helpful in managing data for a statistical analysis such as generalized least squares regression. Only a brief overview of ANNIE/WDM is provided in the attached document. More detailed documentation of ANNIE/WDM is available from the Office of Surface Water. The attached report contains an example of using ANNIE and generalized least squares to develop regression equations for estimating flood discharges and to analyze the regional hydrology network in southeastern Illinois. The regional hydrology network is composed of those stations useful in estimating streamflow characteristics at ungaged sites. A magnetic tape of the ANNIE/GLS programs including the necessary run files, message files, Command Procedure Language (CPL) routines, and test data can be obtained by sending a blank tape to Kate Flynn in the Office of Surface Water (FTS 959-5313 or KMFLYNN@RVARES). Please put your name and address on this tape so that it is easy to identify who sent the tape. The test data and example output are the same as given in the attached report. Technical questions on the generalized least squares regression program should be directed to Gary Tasker, Northeastern Region Research (FTS 959-5892), or Will Thomas, Office of Surface Water (FTS 959-5318). Additional copies of the attached documentation are also available from the Office of Surface Water. Verne R. Schneider Chief, Office of Surface Water Attachment WRD Distribution: FO-LS, SL